Motivated by multi-antennas communication systems, computing capacity (rate-distortion) region of the vector Gaussian channel (source) is of wide interest. One of the most celebrated results is Weingarten et al.'s solution to capacity of the multiple-input multiple-output
(MIMO) Gaussian broadcast channel [1]}. It was pointed out in [2]} that Weingarten's result can be represented as optimization problem involving auxiliary random variables, and the capacity problem is reduced to evaluations of the extremal random variables.
